Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time

Yin Tat Lee; He Sun

Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time

Data Structures and Algorithms 2015-08-14 v1 Discrete Mathematics

Authors: Yin Tat Lee , He Sun

Abstract

We present the first almost-linear time algorithm for constructing linear-sized spectral sparsification for graphs. This improves all previous constructions of linear-sized spectral sparsification, which requires $\Omega(n^2)$ time. A key ingredient in our algorithm is a novel combination of two techniques used in literature for constructing spectral sparsification: Random sampling by effective resistance, and adaptive constructions based on barrier functions.

Keywords

graph spanners graph algorithm sparse optimization

Cite

@article{arxiv.1508.03261,
  title  = {Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time},
  author = {Yin Tat Lee and He Sun},
  journal= {arXiv preprint arXiv:1508.03261},
  year   = {2015}
}

Comments

22 pages. A preliminary version of this paper is to appear in proceedings of the 56th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2015)

Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time

Abstract

Keywords

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